211365169 Kunci Jawaban Dan Pembahasan MAT XIB IPA
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8/18/2019 211365169 Kunci Jawaban Dan Pembahasan MAT XIB IPA
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8/18/2019 211365169 Kunci Jawaban Dan Pembahasan MAT XIB IPA
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1Matematika Kelas XI Program IPA
K o m p e
t e n s
i
D a s a r
M a
t e r i
P o
k o k
/
P e m
b e
l a j a r a n
K e g
i a t a n
P e m
b e
l a j a r a n
I n d i k a
t o r
P e n c a p a
i a n
K o m p e
t e n s
i
P e n
i l a
i a n
T e
k n
i k
B e
n t u k
I n s t r u m e n
C o n
t o h I n s
t r u m e n
A l o k a s
i
W a
k t u
A l a t d a n
S u m
b e r
B e
l a j a r
N i l a
i d a n
M a
t e r i y a n g
D i i n
t e g r a s
i k a n
4 . 1
M e n g g u n a k a n
a l g o r i t m a
p e m b a g i a n
s u k u
b a n y a k
u n t u k m e n e n -
t u k a n h a s i l b a g i
d a n s i s a p e m -
b a g i a n .
S u k u
B a n y a k
S i l a
b u s
B a b I S u
k u
B a n y a
k
S e
k o
l a h
: . . .
K e
l a s
/ S e m e s
t e r
: X I / 2
M a
t a P e
l a j a r a n
: M a
t e m
a t i k a
S t a n
d a r
K o m p e
t e n s
i : 4 .
M
e n g g u n a k a n a t u r a n s u k u b a n y a k d a l a m p e n y e l e s a i a n m a s a l a h .
T e s
4 . 1 . 1
M a m p u m e n d e -
f i n i s i k a n s u k u
b a n y a k .
4 . 1 . 2
M a m p u m e n e n -
t u k a n n i l a i s u k u
b a n y a k .
4 . 1 . 3
M a m p u m e n e n -
t u k a n h a s i l o p e -
r a s i s u k u b a -
n y a k .
4 . 1 . 4
M a m p u m e n e n -
t u k a n h a s i l b a g i
d a n s i s a p e m -
b a g i a n
s u k u
b a n y a k .
T e r t u l i s
1 .
B u k u P R M a
t e -
m a
t i k a
K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n 1 – 2 0
2 .
B u k u P G M a
t e -
m a
t i k a
K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n 1 – 3 8
3 .
B u k u B S E M a
h i r
M e n g e m
b a n g -
k a n
K e m a m p u -
a n
M a
t e m a
t i k a
u n
t u k K e
l a s
X I
S M A / M A I P A ,
W
a h y u d i n
D j u m a n t a d a n
R .
S u d r a j a t ,
D e p d i k n a s
–
M e n j e l a s k a n p e
-
n g e r t i a n s u k u b a n y a k .
–
M e n e n t u k a n u n s u r -
u n s u r s u a t u
s u k u
b a n y a k .
–
M e n e n t u k a n
n i l a
i
s u k u b a n y a k d e n g a n
c a r a s u b s t i t u s i .
–
M e n e n t u k a n
n i l a
i
s u k u b a n y a k d e n g a n
c a r a H o r n e r .
–
M e n e n t u k a n
h a s
i l
p e n j u m l a h a n s u k u
b a n y a k .
–
M e n e n t u k a n h a s i l p e
-
n g u r a n g a n
s u k u
b a n y a k .
–
M e n e n t u k a n h a s i l p e r -
k a l i a n s u k u b a n y a k
.
–
M e n e n t u k a n
h a s
i l
b a g i d a n s i s a p e m
-
b a g i a n s u k u b a n y a
k
d e n g a n
c a r a
b e r -
s u s u n .
( * )
–
M e n e n t u k a n
h a s
i l
b a g i d a n s i s a p e m
-
b a g i a n s u k u b a n y a
k
o l e h ( x – k ) d e n g a n
c a r a H o r n e r . ( * )
–
M e n e n t u k a n
h a s
i l
b a g i d a n s i s a p e m
-
b a g i a n s u k u b a n y a
k
o l e h ( a x + b ) d e n g a n
c a r a H o r n e r .
8 × 4 5
m e n i t
1 .
T e n t u k a n n i l a i s u k u
b a n y a k b e r i k u t u n t u k
n i l a i x y a n g d i s e b u t -
k a n m e n g g u n a k a n
c a r a H o r n e r .
a .
f ( x ) = 3 x
5 –
2 x
4
+ x
2
+ 2 x + 4
u n t u k x = – 2 .
b . g ( x ) = 2 x 4 –
5 x
3
+ x u n t u k x = 3 .
c . p ( x ) = 6 x
3 –
x 2
+
x
+
7
u n t u k
x =
2 .
D i k e t a h u i :
p ( x ) = x 3 +
5 x 2 – 3 x + 1 0
q ( x ) = x 4 –
x 3 +
2 x – 6
T e n t u k a n :
a .
p ( x ) + q ( x ) ,
b .
p ( x ) – q ( x ) ,
c .
4 q ( x ) – 3 p ( x ) .
3 .
T e n t u k a n h a s i l b a g i
d a n s i s a p e m b a g i a n
b e r i k u t .
a .
( 2 x
4 –
3 x
3 +
3 x
2 +
x – 8 ) : ( x –
)
b .
( 4 x
5 –
2 x
3 +
5 x +
6 ) : ( 2 x – 3 )
P e n d i d i k a n
k a r a k t e r
( * ) K r i t i s
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2 Silabus
T e s
T e r t u l i s
4 . 2
M e n g g u n a k a n
t e o r e m a s i s a
d a n
t e o r e m a
f a k t o r d a l a m
p e m e c a h a n
m a s a l a h .
S u k u
B a n y a k
–
M e n e n t u k a n
h a s
i l
b a g i d a n s i s a p e m
-
b a g i a n s u k u b a n y a
k
o l e h a x
2 +
b x + c y a n g
d a p a t
d i f a k t o r k a n
d e n g a n c a r a H o r n e r .
–
M e n j e l a s k a n t e o r e
-
m a s i s a .
–
M e n j e l a s k a n t e o r e
-
m a f a k t o r .
–
M e n e n t u k a n
s i s a
p e m b a g i a n
s u k u
b a n y a k o l e h
s u k u
b a n y a k b e r d e r a j a
t
s a t u .
–
M e n e n t u k a n
s i s a
p e m b a g i a n
s u k u
b a n y a k o l e h
s u k u
b a n y a k b e r d e r a j a
t
d u a d e n g a n m e m i s a
l -
k a n s i s a n y a a x + b .
–
M e n e n t u k a n f a k t o r -
f a k t o r d a r i s u a t u s u k u
b a n y a k .
4 . 2 . 1
M a m p u m e n e n -
t u k a n s i s a p e m -
b a g i a n
s u k u
b a n y a k m e n g -
g u n a k a n t e o r e -
m a s i s a .
4 . 2 . 2
M a m p u m e n e n -
t u k a n
f a k t o r -
f a k t o r
s u a t u
s u k u b a n y a k .
4 .
T e n t u k a n h a s i l b a g i
d a n s i s a p e m b a g i a n
s u k u b a n y a k b e r i k u t .
a .
( 3 x
4 –
2 x
3 +
x 2
– 4 x + 5 ) : ( x – 3 )
( 3 x + 1 )
b .
( 2 x 4 –
3 x 3 +
5 x – 4 )
: ( x 2
– 4 )
1 .
D i k e t a h u i
s u k u
b a n y a k f ( x ) d i b a g i
g ( x ) = x
2 –
4 x + 3
b e r s i s a
2 x
–
4 .
T e n t u k a n :
a . n i l a i f ( 3 ) ;
b . s i s a p e m b a g i a n
f ( x ) o l e h ( x – 1 ) .
2 .
S i s a
p e m b a g i a n
s u k u
b a n y a k
f ( x )
o l e h ( x + 2 ) a d a l a h 8 .
S i s a p e m b a g i a n s u k u
b a n y a k t e r s e b u t o l e h
( 2 x – 1 ) a d a l a h – 4 .
T e n t u k a n s i s a p e m -
b a g i a n s u k u b a n y a k
t e r s e b u t o l e h
2 x
2
+ 3 x – 2 .
3 .
T e n t u k a n
f a k t o r -
f a k t o r
d a r i
s u k u
b a n y a k
f ( x ) = x
4 –
5 x
3 +
2 0 x
– 1 6 .
1 .
B u k u P R M a
t e -
m a
t i k a
K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n 1 – 2 0
2 .
B u k u P G M a
t e -
m a
t i k a
K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n 1 – 3 8
3 .
B u k u B S E M a
h i r
M e n g e m
b a n g -
k a n
K e m a m p u -
a n
M a
t e m a
t i k a
u n
t u k K e
l a s
X I
S M A / M A I P A ,
W
a h y u d i n
D j u m a n t a d a n
R .
S u d r a j a t ,
D e p d i k n a s
8 × 4 5
m e n i t
K o m p e
t e n s
i
D a s a r
M a
t e r i
P o
k o k
/
P e m
b e
l a j a r a n
K e g
i a t a n
P e m
b e
l a j a r a n
I n d i k a
t o r
P e n c a p a
i a n
K o m p e
t e n s
i
P e n
i l a
i a n
T e
k n
i k
B e
n t u k
I n s t r u m e n
C o n
t o h I n s
t r u m e n
A l o k a s
i
W a
k t u
A l a t d a n
S u m
b e r
B e
l a j a r
N i l a
i d a n
M a
t e r i y a n g
D i i n
t e g r a s
i k a n
P e n d i d i k a n
k a r a k t e r
( * ) J u j u r
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3Matematika Kelas XI Program IPA
S i l a
b u s
B a
b I I F u n g s i K
o m p o s
i s i d a n
F u n g s i
I n v e r s
S e
k o
l a h
: . . .
K e
l a s
/ S e m e s
t e r
: X I / 2
M a
t a P e
l a j a r a n
: M a
t e m
a t i k a
S t a n
d a r
K o m p e
t e n s
i : 5 .
M
e n e n t u k a n k o m p o s i s i d u a f u n g s i d a n i n v e r s s u a t u f u n g s i .
K o m p e
t e n s
i
D a s a r
M a
t e r i
P o
k o k
/
P e m
b e
l a j a r a n
K e g
i a t a n
P e m
b e
l a j a r a n
I n d i k a
t o r
P e n c a p a
i a n
K o m p e
t e n s
i
P e n
i l a
i a n
T e
k n
i k
B e
n t u k
I n s t r u m e n
C o n
t o h I n s
t r u m e n
A l o k a s
i
W a
k t u
A l a t d a n
S u m
b e r
B e
l a j a r
N i l a
i d a n
M a
t e r i y a n g
D i i n
t e g r a s
i k a n
5 . 1
M e n e n t u k a n
k o m p o s i s i
f u n g s i d a r i d u a
f u n g s i .
F u n g s i
K o m p o s i s i
2 3
T e s
5 . 1 . 1
M a m p u m e n d e -
f i n i s i k a n f u n g s i .
5 . 1 . 2
M a m p u m e n y e -
l e s a i k a n o p e -
r a s i a l j a b a r f u n g -
s i .
5 . 1 . 3
M a m p u m e n e n -
t u k a n
d a e r a h
a s a l
s u a t u
f u n g s i .
5 . 1 . 4
M a m p u m e n d e -
f i n i s i k a n f u n g s i
k o m p o s i s i .
5 . 1 . 5
M a m p u m e n e n -
t u k a n
f u n g s i
k o m p o s i s i d a r i
d u a a t a u t i g a
f u n g s i .
5 . 1 . 6
M a m p u m e n y e -
l e s a i k a n m a s a -
l a h s e h a r i - h a r i
y a n g m e l i b a t k a n
f u n g s i .
T e r t u l i s
1 .
B u k u P R M a
t e -
m a
t i a K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n 2 1 – 3 6
2 .
B u k u P G M a
t e -
m a
t i k a
K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n 3 9 – 7 0
3 .
B u k u B S E M a
h i r
M e n g e m
b a n g -
k a n
K e m a m p u -
a n
M a
t e m a
t i k a
u n
t u k K e
l a s
X I
S M A / M A I P A ,
W
a h y u d i n
D j u m a n t a d a n
R .
S u d r a j a t ,
D e p d i k n a s
–
M e n j e l a s k a n p e n g e r -
t i a n f u n g s i .
–
M e m b e d a k a n s i f a t -
s i f a t f u n g s i ( f u n g s i
i n j e k t i f , f u n g s i s u r -
j e k t i f , d a n
f u n g s i
b i j e k t i f ) .
–
M e m b e r i k a n c o n t o h
f u n g s i b i j e k t i f .
–
M e n g h i t u n g
s u a t u
n i l a i f u n g s i j i k a d i -
k e t a h u i r u m u s n y a .
–
M e n u l i s k a n r u m u
s
o p e r a s i p e n a m b a h
-
a n , p e n g u r a n g a n
,
p e r k a l i a n ,
d a n p e m
-
b a g i a n d u a f u n g s i .
–
M e n y e l e s a i k a n
o p e r a s i p e n a m b a h
-
a n , p e n g u r a n g a n
,
p e r k a l i a n ,
d a n p e m
-
b a g i a n d u a f u n g s i .
–
M e n y e b u t k a n s y a r a
t
a g a r s u a t u f u n g s i t e r -
d e f i n i s i .
–
M e n y i m p u l k a n d a e r a h
a s a l s u a t u f u n g s i b e r -
d a s a r k a n s y a r a t a g a
r
f u n g s i t e r s e b u t t e r -
d e f i n i s i .
–
M e n e n t u k a n i r i s a n
d a e r a h
a s a l
d u a
f u n g s i .
1 .
D i k e t a h u i f ( x ) = x 2 –
5 ,
( f
g ) ( x ) = 9 x
2 +
1 2 x
– 1 , d a n h ( x ) = x + 1 0 .
R u m u s
f u n g s i
( g
h ) ( x – 1 ) = . . . .
a .
3 x + 3 2
b .
3 x + 2 9
c .
3 x + 2 5
d .
3 x + 1 2
e .
3 x + 2
2 .
D i k e t a h u i
f ( x ) =
+
d a n
g ( x ) =
+ −
.
a .
T e n t u k a n d a e r a h
a s a l f u n g s i h ( x )
j i k a h ( x ) =
.
b .
T e n t u k a n d a e r a h
a s a l f u n g s i k ( x )
j i k a k ( x ) =
.
8 × 4 5
m e n i t
P e n d i d i k a n
k a r a k t e r
( * ) K r i t i s
8/18/2019 211365169 Kunci Jawaban Dan Pembahasan MAT XIB IPA
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4 Silabus
T e s
T e r t u l i s
5 . 2
M e n e n t u k a n
i n v e r s
s u a t u
f u n g s i .
F u n g s i
I n v e r s
–
M e n j e l a s k a n p e n g e r -
t i a n f u n g s i k o m p o s i s
i .
–
M e n j e l a s k a n s i f a t -
s i f a t k o m p o s i s i f u n g s
i .
( * )
–
M e n u l i s k a n
r u m u
s
f u n g s i k o m p o s i s i d a
r i
d u a a t a u t i g a f u n g s i .
–
M e n g h i t u n g s u a t u n i l a i
f u n g s i k o m p o s i s i d a
r i
d u a a t a u t i g a f u n g s i .
–
M e n u l i s k a n
r u m u
s
f u n g s i y a n g t e r m u a t
d a l a m s o a l c e r i t a .
–
M e n g h i t u n g
s u a t
u
n i l a i f u n g s i y a n g t e r -
m u a t d a l a m s o a l c e r i t a .
–
M e n j e l a s k a n p e n g e r -
t i a n f u n g s i i n v e r s .
–
M e n j e l a s k a
n
l a n g k a h - l a n g k a
h
m e n e n t u k a n i n v e r
s
s u a t u f u n g s i .
–
M e n e n t u k a n i n v e r
s
s u a t u f u n g s i s e s u a i
l a n g k a h - l a n g k a
h
y a n g d i p e l a j a r i .
( * )
–
M e n e n t u k a n i n v e r
s
s u a t u f u n g s i d e n g a
n
r u m u s p r a k t i s .
–
M e n g h i t u n g
s u a t
u
n i l a i i n v e r s f u n g s i .
–
M e n g g a m b a r g r a f i k
i n v e r s s u a t u f u n g s i .
–
M e n j e l a s k a n p e n g e r -
t i a n i n v e r s d a r i f u n g s i
k o m p o s i s i .
–
M e n e n t u k a n i n v e r
s
s u a t u f u n g s i k o m p o
-
s i s i
b e r d a s a r k a
n
p e n g e r t i a n n y a .
5 . 2 . 1
M a m p u m e n d e -
f i n i s i k a n f u n g s i
i n v e r s .
5 . 2 . 2
M a m p u m e n e n -
t u k a n
i n v e r s
s u a t u f u n g s i .
5 . 2 . 3
M a m p u m e n d e -
f i n i s i k a n i n v e r s
d a r i f u n g s i k o m -
p o s i s i .
5 . 2 . 4
M a m p u m e n e n -
t u k a n
i n v e r s
s u a t u
f u n g s i
k o m p o s i s i .
5 . 2 . 5
M a m p u m e n y e -
l e s a i k a n m a s a -
l a h s e h a r i - h a r i
y a n g m e l i b a t k a n
i n v e r s
s u a t u
f u n g s i .
1 .
B u k u P R M a
t e -
m a
t i k a
K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n 2 1 – 3 6
2 .
B u k u P G M a
t e -
m a
t i k a
K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n 3 9 – 7 0
3 .
B u k u B S E M a
h i r
M e n g e m
b a n g -
k a n
K e m a m p u -
a n
M a
t e m a
t i k a
u n
t u k K e
l a s
X I
S M A / M A I P A ,
W
a h y u d i n
D j u m a n t a d a n
R .
S u d r a j a t ,
D e p d i k n a s
8 × 4 5
m e n i t
3 .
D i b e r i k a n
f u n g s i
f ( x ) = x
2 –
2 x – 4 ,
g ( x ) = 3 x + 9 ,
d a n
( g
f ) ( a ) = 6 .
a .
T e n t u k a n n i l a i a
j i k a
a
a d a l a h
b i l a n g a n p o s i t i f .
b .
T e n t u k a n
n i l a i
( f
g ) ( 2 ) .
1 .
I n v e r s d a r i f u n g s i
h ( x ) =
+ −
+
2
a d a l a h . . . .
a .
h – 1 ( x ) =
+ −
;
x ≠ 2
b .
h – 1 ( x ) =
+ +
;
x ≠ – 2
c .
h – 1 ( x ) =
+ −
;
x ≠ 4
d .
h – 1 ( x ) =
− −
;
x ≠ 4
e .
h – 1 ( x ) =
− +
;
x ≠ – 4
2 .
D i k e t a h u i f ( x ) = 1 2 x + 1
d a n
g ( x ) =
−
;
x ≠ 3 .
D a e r a h a s a l
f u n g s i ( g
f ) – 1
a d a l a h
. . . .
K o m p e
t e n s
i
D a s a r
M a
t e r i
P o
k o k
/
P e m
b e
l a j a r a n
K e g
i a t a n
P e m
b e
l a j a r a n
I n d i k a
t o r
P e n c a p a
i a n
K o m p e
t e n s
i
P e n
i l a
i a n
T e
k n
i k
B e
n t u k
I n s t r u m e n
C o n
t o h I n s
t r u m e n
A l o k a s
i
W a
k t u
A l a t d a n
S u m
b e r
B e
l a j a r
N i l a
i d a n
M a
t e r i y a n g
D i i n
t e g r a s
i k a n
P e n d i d i k a n
k a r a k t e r
( * ) T e l i t i
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5Matematika Kelas XI Program IPA
–
M e n e n t u k a n i n v e r
s
s u a t u f u n g s i k o m p o
-
s i s i d e n g a n
c a r
a
y a n g s a m a d e n g a
n
m e n e n t u k a n i n v e r
s
s u a t u f u n g s i .
–
M e n g h i t u n g
s u a t
u
n i l a i i n v e r s f u n g s i
k o m p o s i s i .
–
M e n u l i s k a n
r u m u
s
i n v e r s s u a t u f u n g s i
y a n g t e r m u a t d a l a m
s o a l c e r i t a .
–
M e n g h i t u n g
n i l a i
i n v e r s s u a t u f u n g s i
d a l a m s o a l c e r i t a .
K o m p e
t e n s
i
D a s a r
M a
t e r i
P o
k o k
/
P e m
b e
l a j a r a n
K e g
i a t a n
P e m
b e
l a j a r a n
I n d i k a
t o r
P e n c a p a
i a n
K o m p e
t e n s
i
P e n
i l a
i a n
T e
k n
i k
B e
n t u k
I n s t r u m e n
C o n
t o h I n s
t r u m e n
A l o k a s
i
W a
k t u
A l a t d a n
S u m
b e r
B e
l a j a r
N i l a
i d a n
M a
t e r i y a n g
D i i n
t e g r a s
i k a n
a .
{ x | x ≠ –
, x ∈ R }
b .
{ x | x ≠ –
, x ∈ R }
c .
{ x | x ≠ 0 , x ∈ R }
d .
{ x | x ≠
, x ∈ R }
e .
{ x | x ≠ 1 , x ∈ R }
3 .
D i k e t a h u i f ( x ) = 2 x + 1 3
d a n g – 1 ( x + 1 ) = 1 2 x – 7 .
T e n t u k a n :
a . g – 1 ( x )
b .
f – 1 ( x )
c .
( f
g ) – 1 ( x )
d .
( g
f ) – 1 ( x )
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6 Silabus
T e s
6 . 1
M e n j e l a s k a n
s e c a r a i n t u i t i f
a r t i l i m i t f u n g s i
d i s u a t u t i t i k
d a n d i t a k h i n g -
g a .
L i m i t F u n g s i
6 . 1 . 1
M a m p u m e n d e -
f i n i s i k a n
l i m i t
f u n g s i d i s u a t u
t i t i k .
6 . 1 . 2
M a m p u m e n e n -
t u k a n n i l a i l i m i t
f u n g s i b e r d a s a r -
k a n
g a m b a r
g r a f i k f u n g s i .
6 . 1 . 3
M a m p u m e n d e -
f i n i s i k a n
l i m i t
f u n g s i d i t a k
h i n g g a .
6 . 1 . 4
M a m p u m e n e n -
t u k a n l i m i t f u n g s i
d i t a k
h i n g g a
b e r d a s a r k a n
g a m b a r g r a f i k
f u n g s i .
T e r t u l i s
1 .
B u k u P R M a
t e -
m a
t i k a
K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n 4 1 – 5 8
2 .
B u k u P G M a
t e -
m a
t i k a
K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n
8 3 –
1 2 3
3 .
B u k u B S E M a
h i r
M e n g e m
b a n g -
k a n
K e m a m p u -
a n
M a
t e m a
t i k a
u n
t u k K e
l a s
X I
S M A / M A I P A ,
W
a h y u d i n
D j u m a n t a d a n
R .
S u d r a j a t ,
D e p d i k n a s
–
M e n j e l a s k a n p e
-
n g e r t i a n l i m i t f u n g s i d i
s u a t u
t i t i k
s e c a r
a
i n t u i t i f .
–
M e n e n t u k a n n i l a i l i m
i t
f u n g s i d i s u a t u t i t i k
j i k a d i d e k a t i d a r i k i r i
b e r d a s a r k a n g a m b a
r
g r a f i k f u n g s i .
–
M e n e n t u k a n n i l a i l i m
i t
f u n g s i d i s u a t u t i t i k
j i k a
d i d e k a t i d a r i
k a n a n b e r d a s a r k a
n
g a m b a r g r a f i k f u n g s
i .
–
M e n e n t u k a n
l i m
i t
f u n g s i d i s u a t u t i t i k
b e r d a s a r k a n g a m b a
r
g r a f i k f u n g s i .
–
M e n j e l a s k a n p e n g e r -
t i a n l i m i t f u n g s i d i t a
k
h i n g g a s e c a r a i n t u i t i f .
–
M e n e n t u k a n n i l a i l i m
i t
f u n g s i j i k a v a r i a b e l
m e m b e s a r
t a n p
a
b a t a s b e r d a s a r k a
n
g a m b a r g r a f i k f u n g s
i .
–
M e n e n t u k a n n i l a i l i m
i t
f u n g s i j i k a v a r i a b e l
m e n g e c i l t a n p a b a t a
s
b e r d a s a r k a n g a m b a
r
g r a f i k f u n g s i .
8 × 4 5
m e n i t
U n
t u k m e n
j a w a
b
s o a
l
n o m o r
1 s a m p a
i d e n g a n
3
p e r h a
t i k a n
g a m
b a r
g r a
f i k f u n g s
i f ( x
) b e r i
k u
t .
1 .
→
f ( x ) = . . .
a .
1
d .
3
b .
1
e .
3
c .
2
2 .
→ → → →
f ( x ) = . . .
a .
0
d .
1
b .
1
e .
t i d a k
c .
2
a d a
3 .
→
∞
f ( x ) = . . .
a . – ∞
d . ∞
b . – 2
e .
t i d a k
c .
0
a d a
S i l a
b u s
B a b I I I L i m i t F u n g s
i
S e
k o
l a h
: . . .
K e
l a s
/ S e m e s
t e r
: X I / 2
M a
t a P e
l a j a r a n
: M a
t e m
a t i k a
S t a n
d a r
K o m p e
t e n s
i : 6 .
M
e n g g u n a k a n k o n s e p l i m i t f u n g s i d a n t u r u n a n f u n g s i d a l a m p e m e c a h a n
m a s a l a h .
K o m p e
t e n s
i
D a s a r
M a
t e r i
P o
k o k
/
P e m
b e
l a j a r a n
K e g
i a t a n
P e m
b e
l a j a r a n
I n d i k a
t o r
P e n c a p a
i a n
K o m p e
t e n s
i
P e n
i l a
i a n
T e
k n
i k
B e
n t u k
I n s t r u m e n
C o n
t o h I n s
t r u m e n
A l o k a s
i
W a
k t u
A l a t d a n
S u m
b e r
B e
l a j a r
N i l a
i d a n
M a
t e r i y a n g
D i i n
t e g r a s
i k a n
X
Y
6 5 4 3 2 1
– 3 – 2 – 1 0
1
2
3
4
5
6
– 1
– 2
f ( x )
P e n d i d i k a n
k a r a k t e r
( * ) K e r j a
k e r a s
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7Matematika Kelas XI Program IPA
T e s
T e r
t u l i s
6 . 2
M e n g g u n a k a n
s i f a t l i m i t f u n g s i
u n t u k
m e n g -
h i t u n g b e n t u k
t a k t e n t u f u n g s i
a l j a b a r d a n t r i -
g o n o m e t r i .
L i m i t F u n g s i
–
M e n j e l a s k a n s i f a t -
s i f a t l i m i t f u n g s i d i
s a t u t i t i k .
–
M e n j e l a s k a n
c a r
a
m e n y e l e s a i k a n l i m
i t
f u n g s i d i s u a t u t i t i k
m e n g g u n a k a n c a r
a
s u b s t i t u s i l a n g s u n g .
–
M e n j e l a s k a n
c a r
a
m e n y e l e s a i k a n l i m
i t
f u n g s i d i s u a t u t i t i k
m e n g g u n a k a n c a r
a
m e m f a k t o r k a n .
–
M e n j e l a s k a n
c a r
a
m e n y e l e s a i k a n l i m
i t
f u n g s i d i s u a t u t i t i k
d e n g a n m e n g a l i k a
n
b e n t u k s e k a w a n .
–
M e n g g u n a k a n s i f a t -
s i f a t l i m i t u n t u k m e n g
-
h i t u n g l i m i t f u n g s i .
–
M e n y e l e s a i k a n p e r -
m a s a l a h a n y a n g b e r -
k a i t a n d e n g a n l i m
i t
f u n g s i d i s u a t u t i t i k .
–
M e n j e l a s k a n s i f a t -
s i f a t l i m i t f u n g s i d i t a
k
h i n g g a .
–
M e n j e l a s k a n
c a r
a
m e n y e l e s a i k a n l i m
i t
f u n g s i d i t a k h i n g g
a
m e n g g u n a k a n c a r
a
s u b s t i t u s i l a n g s u n g .
–
M e n j e l a s k a n
c a r
a
m e n y e l e s a i k a n l i m
i t
f u n g s i d i t a k h i n g g
a
m e n g g u n a k a n c a r
a
m e m b a g i
d e n g a
n
p a n g k a t t e r t i n g g i .
–
M e n j e l a s k a n
c a r
a
m e n y e l e s a i k a n l i m
i t
f u n g s i d i t a k h i n g g
a
m e n g g u n a k a n c a r
a
m e n g a l i k a n d e n g a
n
b e n t u k s e k a w a n .
6 . 2 . 1
M a m p u m e n e n -
t u k a n n i l a i l i m i t
f u n g s i a l j a b a r d i
s u a t u t i t i k .
6 . 2 . 2
M a m p u m e n y e -
l e s a i k a n p e r m a -
s a l a h a n
y a n g
b e r k a i t a n
d e -
n g a n l i m i t f u n g s i
d i s u a t u t i t i k .
6 . 2 . 3
M a m p u m e n e n -
t u k a n n i l a i l i m i t
f u n g s i a l j a b a r d i
t a k h i n g g a .
6 . 2 . 4
M a m p u m e n y e -
l e s a i k a n p e r m a -
s a l a h a n
y a n g
b e r k a i t a n
d e -
n g a n l i m i t f u n g s i
d i t a k h i n g g a .
6 . 2 . 5
M a m p u m e n e n -
t u k a n n i l a i l i m i t
f u n g s i t r i g o n o -
m e t r i d i s u a t u
t i t i k .
6 . 2 . 6
M a m p u m e n y e -
l e s a i k a n p e r m a -
s a l a h a n
y a n g
b e r k a i t a n
d e -
n g a n l i m i t f u n g s i
t r i g o n o m e t r i .
1 .
B u k u P R M a
t e -
m a
t i k a
K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n 4 1 – 5 8
2 .
B u k u P G M a
t e -
m a
t i k a
K e
l a s
X I
S e m e s
t e r
2 ,
I n t a n P a r i w a r a ,
h a l a m a n
8 3 –
1 2 8
3 .
B u k u B S E M a
h i r
M e n g e m
b a n g -
k a n
K e m a m p u -
a n
M a
t e m a
t i k a
u n
t u k K e
l a s
X I
S M A / M A I P A ,
W
a h y u d i n
D j u m a n t a d a n
R .
S u d r a j a t ,
D e p d i k n a s
1 .
N i l a i
→ → → →
− − − −
− − − −
− − − −
= . . . .
a .
d .
4
b .
e . ∞
c .
2
2 .
J i k a
→
=
4 ,
n i l a i a y a n g m e m e -
n u h i a d a l a h . . . .
a .
2
d . – 1
b .
1
e . – 2
c .
0
3 .
N i l a i
→
∞ ∞ ∞ ∞ ( ( x – 2 )
–
−
) = . . .
a . – 4
d .
0
b . – 3
e .
4
c . – 2
4 .
→
= . . .
a .
5
d .
b .
e .
c .
5 .
T e n t u k a n n i l a i l i m i t
b e r i k u t .
a .
→ → → →
− −
b .
→
−
−
−
1 2 × 4 5
m e n i t
K o m p e
t e n s
i
D a s a r
M a
t e r i
P o
k o k
/
P e m
b e
l a j a r a n
K e g
i a t a n
P e m
b e
l a j a r a n
I n d i k a
t o r
P e n c a p a
i a n
K o m p e
t e n s
i
P e n
i l a
i a n
T e
k n
i k
B e
n t u k
I n s t r u m e n
C o n
t o h I n s
t r u m e n
A l o k a s
i
W a
k t u
A l a t d a n
S u m
b e r
B e
l a j a r
N i l a
i d a n
M a
t e r i y a n g
D i i n
t e g r a s
i k a n
P e n d i d i k a n
k a r a k t e r
( * ) R a s a
I n g i n
T a h u
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8 Silabus
K o m p e
t e n s
i
D a s a r
M a
t e r i
P o
k o k
/
P e m
b e
l a j a r a n
K e g
i a t a n
P e m
b e
l a j a r a n
I n d i k a
t o r
P e n c a p a
i a n
K o m p e
t e n s
i
P e n
i l a
i a n
T e
k n
i k
B e
n t u k
I n s t r u m e n
C o n
t o h I n s
t r u m e n
A l o k a s
i
W a
k t u
A l a t d a n
S u m
b e r
B e
l a j a r
N i l a
i d a n
M a
t e r i y a n g
D i i n
t e g r a s
i k a n
6 .
J i k a
→
∞
(
+ + + +
–
( 2 x – 1 ) ) =
, c a r i l a h
n i l a i a y a n g m e m e -
n u h i .
7 .
T e n t u k a n n i l a i l i m i t
b e r i k u t .
a .
→
− − − −
b .
→ → → →
− − − −
–
M e n y e l e s a i k a n p e r -
m a s a l a h a n y a n g b e r -
k a i t a n d e n g a n l i m
i t
f u n g s i d i t a k h i n g g a .
–
M e n j e l a s k a n t e o r e m a
l i m i t a p i t .
–
M e n j e l a s k a n
c a r a
m e n y e l e s a i k a n l i m
i t
f u n g s i t r i g o n o m e t r i .
–
M e n e n t u k a n n i l a i l i m
i t
f u n g s i t r i g o n o m e t r i d i
t i t i k n o l .
–
M e n j e l a s k a n
c a r a
m e n y e l e s a i k a n l i m
i t
f u n g s i t r i g o n o m e t r i d i
s u a t u t i t i k .
–
M e n e n t u k a n n i l a i l i m
i t
f u n g s i t r i g o n o m e t r i d i
s u a t u t i t i k .
–
M e n y e l e s a i k a n p e r -
m a s a l a h a n y a n g b e r -
k a i t a n d e n g a n l i m
i t
f u n g s i t r i g o n o m e t r i .
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8/18/2019 211365169 Kunci Jawaban Dan Pembahasan MAT XIB IPA
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10 Silabus
3 .
J i k a f ( x ) = ( x + 1 )
+ + + +
m a k a f ′ ( x ) =
. . . .
a .
+ +
b .
+ +
c .
+ +
d .
+ +
e .
+ +
4 .
D i k e t a h u i
g ( x ) =
−
. N i l a i
g (
+ + + +
) = . . . .
a .
−
d . –
b .
+
e . –
c .
5 .
J i k a f ( x ) =
+ + + +
,
g ( x ) =
− − − −
, d a n
h = g
f , t u r u n a n d a r i
h a d a l a h . . . .
a .
+ + + +
b .
+ + + +
c .
+ + + +
d .
+ + + +
e .
+ + + +
K o m p e
t e n s
i
D a s a r
M a
t e r i
P o
k o k
/
P e m
b e
l a j a r a n
K e g
i a t a n
P e m
b e
l a j a r a n
I n d i k a
t o r
P e n c a p a
i a n
K o m p e
t e n s
i
P e n
i l a
i a n
T e
k n
i k
B e
n t u k
I n s t r u m e n
C o n
t o h I n s
t r u m e n
A l o k a s
i
W a
k t u
A l a t d a n
S u m
b e r
B e
l a j a r
N i l a
i d a n
M a
t e r i y a n g
D i i n
t e g r a s
i k a n
8/18/2019 211365169 Kunci Jawaban Dan Pembahasan MAT XIB IPA
12/131
11Matematika Kelas XI Program IPA
2 × 4 5
m e n i t
6 .
D i k e t a h u i
f ( x )
=
a x
2 +
b x + 6 .
J i k a
f ′ ( – 1 ) =
– 1 1
d a n
f ′ ( 2 ) = 7 ,
t e n t u k a n
n i l a i f ( 1 ) .
7 .
D i k e t a h u i y = 3 t 2
d a n
x = 2 t 2
+ t – 1 .
J i k a
t < 0 ,
t e n t u k a n n i l a i
d
i x = 2 .
1 .
J i k a y = c o s
4 x
m a k a
= . . . .
a .
t a n x
b .
2 t a n x
c . – 4 t a n x
d . – 2 c o t a n x
e . – 4 c o t a n x
2 .
D i k e t a h u i
g ( x ) =
− − − −
. N i l a i
( g (
π ) ) = . . . .
a .
1
d . –
b .
e . – 1
c .
0
3 .
D i k e t a h u i f ( x ) = s i n
2 x
d a n f ′ ′ ( x ) = 1 u n t u k
0 ° ≤ x ≤ 1 8 0 ° . N i l a i x
y a n g m e m e n u h i a d a -
l a
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